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Extensions 1→N→G→Q→1 with N=C12 and Q=C4⋊C4

Direct product G=N×Q with N=C12 and Q=C4⋊C4
dρLabelID
C12×C4⋊C4192C12xC4:C4192,811

Semidirect products G=N:Q with N=C12 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C12⋊1(C4⋊C4) = C12⋊(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12:1(C4:C4)192,531
C12⋊2(C4⋊C4) = (C4×Dic3)⋊8C4φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12:2(C4:C4)192,534
C12⋊3(C4⋊C4) = C4⋊C4⋊6Dic3φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12:3(C4:C4)192,543
C12⋊4(C4⋊C4) = C12⋊4(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:4(C4:C4)192,487
C12⋊5(C4⋊C4) = C42⋊10Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:5(C4:C4)192,494
C12⋊6(C4⋊C4) = C4×Dic3⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:6(C4:C4)192,490
C12⋊7(C4⋊C4) = C4×C4⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:7(C4:C4)192,493
C12⋊8(C4⋊C4) = C3×C42⋊9C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:8(C4:C4)192,817
C12⋊9(C4⋊C4) = C3×C23.65C23φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12:9(C4:C4)192,822

Non-split extensions G=N.Q with N=C12 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C12.1(C4⋊C4) = C8.Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.1(C4:C4)192,46
C12.2(C4⋊C4) = C6.6D16φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.2(C4:C4)192,48
C12.3(C4⋊C4) = C6.SD32φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.3(C4:C4)192,49
C12.4(C4⋊C4) = C24.7Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C12964C12.4(C4:C4)192,52
C12.5(C4⋊C4) = C24.6Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.5(C4:C4)192,53
C12.6(C4⋊C4) = C12.C42φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.6(C4:C4)192,88
C12.7(C4⋊C4) = C12.(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.7(C4:C4)192,89
C12.8(C4⋊C4) = C12.2C42φ: C4⋊C4/C22 → C22 ⊆ Aut C1248C12.8(C4:C4)192,91
C12.9(C4⋊C4) = M4(2)⋊Dic3φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.9(C4:C4)192,113
C12.10(C4⋊C4) = C12.3C42φ: C4⋊C4/C22 → C22 ⊆ Aut C1248C12.10(C4:C4)192,114
C12.11(C4⋊C4) = (C2×C24)⋊C4φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.11(C4:C4)192,115
C12.12(C4⋊C4) = C12.20C42φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.12(C4:C4)192,116
C12.13(C4⋊C4) = M4(2)⋊4Dic3φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.13(C4:C4)192,118
C12.14(C4⋊C4) = C2×C6.Q16φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.14(C4:C4)192,521
C12.15(C4⋊C4) = C2×C12.Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.15(C4:C4)192,522
C12.16(C4⋊C4) = C4⋊C4.225D6φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.16(C4:C4)192,523
C12.17(C4⋊C4) = (C4×Dic3)⋊9C4φ: C4⋊C4/C22 → C22 ⊆ Aut C12192C12.17(C4:C4)192,536
C12.18(C4⋊C4) = C42.43D6φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.18(C4:C4)192,558
C12.19(C4⋊C4) = Dic3⋊4M4(2)φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.19(C4:C4)192,677
C12.20(C4⋊C4) = C12.88(C2×Q8)φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.20(C4:C4)192,678
C12.21(C4⋊C4) = C23.52D12φ: C4⋊C4/C22 → C22 ⊆ Aut C1296C12.21(C4:C4)192,680
C12.22(C4⋊C4) = C23.9Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C12484C12.22(C4:C4)192,684
C12.23(C4⋊C4) = C48⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.23(C4:C4)192,63
C12.24(C4⋊C4) = C48⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.24(C4:C4)192,64
C12.25(C4⋊C4) = C48.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12962C12.25(C4:C4)192,65
C12.26(C4⋊C4) = C24.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.26(C4:C4)192,72
C12.27(C4⋊C4) = C12.8C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1248C12.27(C4:C4)192,82
C12.28(C4⋊C4) = C42⋊3Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.28(C4:C4)192,90
C12.29(C4⋊C4) = (C2×C12).Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.29(C4:C4)192,92
C12.30(C4⋊C4) = C12.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.30(C4:C4)192,110
C12.31(C4⋊C4) = C12⋊7M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.31(C4:C4)192,483
C12.32(C4⋊C4) = C42⋊11Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.32(C4:C4)192,495
C12.33(C4⋊C4) = C4⋊C4.232D6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.33(C4:C4)192,554
C12.34(C4⋊C4) = Dic3⋊C8⋊C2φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.34(C4:C4)192,661
C12.35(C4⋊C4) = C2×C8⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.35(C4:C4)192,663
C12.36(C4⋊C4) = C2×C24⋊1C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.36(C4:C4)192,664
C12.37(C4⋊C4) = C23.8Dic6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.37(C4:C4)192,683
C12.38(C4⋊C4) = C12⋊C16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.38(C4:C4)192,21
C12.39(C4⋊C4) = C24.1C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12482C12.39(C4:C4)192,22
C12.40(C4⋊C4) = Dic3⋊C16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.40(C4:C4)192,60
C12.41(C4⋊C4) = C24.97D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.41(C4:C4)192,70
C12.42(C4⋊C4) = (C2×C12)⋊3C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.42(C4:C4)192,83
C12.43(C4⋊C4) = (C2×C24)⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.43(C4:C4)192,109
C12.44(C4⋊C4) = C2×C12⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.44(C4:C4)192,482
C12.45(C4⋊C4) = C4⋊C4.234D6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.45(C4:C4)192,557
C12.46(C4⋊C4) = C2×Dic3⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.46(C4:C4)192,658
C12.47(C4⋊C4) = C23.27D12φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.47(C4:C4)192,665
C12.48(C4⋊C4) = C2×C24.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.48(C4:C4)192,666
C12.49(C4⋊C4) = C2×C12.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.49(C4:C4)192,682
C12.50(C4⋊C4) = C3×C4.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.50(C4:C4)192,143
C12.51(C4⋊C4) = C3×C42⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1248C12.51(C4:C4)192,145
C12.52(C4⋊C4) = C3×C22.4Q16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.52(C4:C4)192,146
C12.53(C4⋊C4) = C3×C22.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.53(C4:C4)192,149
C12.54(C4⋊C4) = C3×M4(2)⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.54(C4:C4)192,150
C12.55(C4⋊C4) = C3×C8.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.55(C4:C4)192,171
C12.56(C4⋊C4) = C3×C16⋊3C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.56(C4:C4)192,172
C12.57(C4⋊C4) = C3×C16⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.57(C4:C4)192,173
C12.58(C4⋊C4) = C3×C8.4Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12962C12.58(C4:C4)192,174
C12.59(C4⋊C4) = C3×C42⋊8C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.59(C4:C4)192,815
C12.60(C4⋊C4) = C3×C4⋊M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.60(C4:C4)192,856
C12.61(C4⋊C4) = C3×C42.6C22φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.61(C4:C4)192,857
C12.62(C4⋊C4) = C6×C4.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.62(C4:C4)192,858
C12.63(C4⋊C4) = C6×C2.D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12192C12.63(C4:C4)192,859
C12.64(C4⋊C4) = C3×M4(2)⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C1296C12.64(C4:C4)192,861
C12.65(C4⋊C4) = C3×M4(2).C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C12484C12.65(C4:C4)192,863
C12.66(C4⋊C4) = C3×C22.7C42central extension (φ=1)192C12.66(C4:C4)192,142
C12.67(C4⋊C4) = C3×C4⋊C16central extension (φ=1)192C12.67(C4:C4)192,169
C12.68(C4⋊C4) = C3×C8.C8central extension (φ=1)482C12.68(C4:C4)192,170
C12.69(C4⋊C4) = C6×C4⋊C8central extension (φ=1)192C12.69(C4:C4)192,855
C12.70(C4⋊C4) = C3×C23.25D4central extension (φ=1)96C12.70(C4:C4)192,860
C12.71(C4⋊C4) = C6×C8.C4central extension (φ=1)96C12.71(C4:C4)192,862

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